Investors were cheered by recent news that weekly claims for unemployment benefits fell to 339,000, a surprisingly large drop of 16,000 from the week before. Economists had been expecting about 350,000 jobless claims. The number of people applying for unemployment insurance has now fallen to the levels of early 2008, when hardly anybody knew a brutal recession was brewing.

The lower number means fewer people are getting laid off, probably because many companies have cut as much as they can and conditions aren't dire enough to cut more. But it may still be a while before fewer layoffs transitions to a big uptick in hiring.

The unemployment report for April, which the Labor Department will release on May 2, is expected to show that employers added about 145,000 new jobs this month. That's better than nothing, but it's a fairly low number. In general, it takes job gains of about 200,000 per month or more to lower the unemployment rate and keep employment steady with population growth.

Still, if there's any job growth in April, it will be welcome, because economists and business leaders remain worried about how severely the federal spending cuts known as the sequester will harm the economy. Since the cuts went into effect March 1, and are being phased in, the impact is just now beginning to show up in economic data. While the effect has been muted so far, many economists say there's no way to avoid the pain that will come from about $85 billion in reduced government spending.

"The economy hit a soft patch in March that will likely persist for a couple of quarters," forecasting firm IHS Global Insight said recently.

The April job numbers will be the biggest clue yet how hard the sequester will bite. Some economists have predicted job growth in April and May could be as low as zero, which would be a grim development likely to shock investors who have been increasingly optimistic about the economy. Many stock-market analysts have been predicting a 5 or 10 percent correction, and a sour jobs report on May 2 could be the thing that triggers it.

The latest jobless claims, however, suggest that the job market, somehow, is holding up better than it ought to be. What seems to be happening is that companies have stopped firing but are still a long way from hiring. "Firms may be ratcheting back on hiring plans in anticipation of weaker demand this spring and summer because of the fiscal restraint," says Moody's Analytics. "Firms' reluctance to hire will cause job growth to weaken this quarter."

So the job market appears to be improving at the same time it's not. If you have a job, that's no big deal. If you're looking for one, progress is maddeningly slow.

Rick Newman's latest book is Rebounders: How Winners Pivot From Setback To Success. Follow him on Twitter: @rickjnewman.